Refer to TS 36.321 6.1.3 MAC Control Elements for the details.
When we say 'communication between UE and Network', we normally think about only signaling message (RRC or NAS message). When I say 'communication' in this case, it means 'control command exchange' between UE and network, not the data traffic.
In UMTS case, it is true that only RRC and NAS message functions as communication between UE and Network, but in LTE case there are several communication path at MAC layer. It implies that there are special MAC structure that carries special control information. These special MAC structure carrying the control information is called 'MAC CE', which means 'MAC Control Element'.
There are several MAC CE in downlink MAC and also several MAC CE in uplink MAC. Following table from 36.213 shows the LCID types of MAC header. The parts marked in red rectangle is LCID representing various MAC CE.
Values of LCID for DL-SCH
Values of LCID for UL-SCH
